Superconvergence and extrapolation analysis of a nonconforming mixed finite element approximation for time-harmonic Maxwell's equations (Q639392)

In the first part of the present paper, based on the mixed formulation of time-harmonic Maxwell's equations, a new nonconforming mixed finite element approximation to the three-dimensional time-harmonic Maxwell's equations is proposed. Next, the behavior of the asymptotic expansion for the interpolation error and the nonconforming error of the nonconforming mixed finite element is presented. The authors also develop a superclose and a superconvergence analysis of the electric field and of the magnetic field. In the final part of this paper, the accuracy is improved by an extrapolation method. In this case, \(O(h^4)\) approximations in the sense of the \(L^2\)-norm are derived.